Journal of Statistical Physics

, Volume 142, Issue 3, pp 524–576 | Cite as

Layering and Wetting Transitions for an SOS Interface

  • Kenneth S. Alexander
  • François DunlopEmail author
  • Salvador Miracle-Solé


We study the solid-on-solid interface model above a horizontal wall in three dimensional space, with an attractive interaction when the interface is in contact with the wall, at low temperatures. There is no bulk external field. The system presents a sequence of layering transitions, whose levels increase with the temperature, before reaching the wetting transition.


SOS model Wetting Layering transitions Interface Entropic repulsion 


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  1. 1.
    Alexander, K.S., Dunlop, F., Miracle-Sole, S.: Layering in the Ising model. J. Stat. Phys. 141, 217–241 (2010) zbMATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Basuev, A.G.: Ising model in half-space: a series of phase transitions in low magnetic fields. Theor. Math. Phys. 153, 1539–1574 (2007) zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bissacot, R., Fernandez, R., Procacci, A.: On the convergence of cluster expansions for polymer gases. J. Stat. Phys. 139, 598–617 (2010) zbMATHCrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Binder, K., Landau, D.P.: Wetting versus layering near the roughening transition in the 3d Ising model. Phys. Rev. B 46, 4844 (1992) CrossRefADSGoogle Scholar
  5. 5.
    Cesi, F., Martinelli, F.: On the layering transition of an SOS interface interacting with a wall. I. Equilibrium results. J. Stat. Phys. 82, 823–913 (1996) zbMATHCrossRefMathSciNetADSGoogle Scholar
  6. 6.
    Chalker, J.T.: The pinning of an interface by a planar defect. J. Phys. A: Math. Gen. 15, L481–L485 (1982) CrossRefMathSciNetADSGoogle Scholar
  7. 7.
    Dobrushin, R.L.: Estimates of semi-invariants for the Ising model at low temperatures. In: Topics in Statistics and Theoretical Physics. Amer. Math. Soc. Transl. (2), vol. 177, pp. 59–81 (1996) Google Scholar
  8. 8.
    Dinaburg, E.I., Mazel, A.E.: Layering transition in SOS model with external magnetic field. J. Stat. Phys. 74, 533–563 (1996) CrossRefMathSciNetADSGoogle Scholar
  9. 9.
    Fröhlich, J., Pfister, C.E.: The wetting and layering transitions in the half-infinite Ising model. Europhys. Lett. 3, 845–852 (1987) CrossRefADSGoogle Scholar
  10. 10.
    Fröhlich, J., Pfister, C.E.: Semi-infinite Ising model: I. Thermodynamic functions and phase diagram in absence of magnetic field. Commun. Math. Phys. 109, 493–523 (1987) CrossRefADSGoogle Scholar
  11. 11.
    Fröhlich, J., Pfister, C.E.: Semi-infinite Ising model: II. The wetting and layering transitions. Commun. Math. Phys. 112, 51–74 (1987) zbMATHCrossRefADSGoogle Scholar
  12. 12.
    Gallavotti, G., Martin-Lof, A., Miracle-Sole, S.: Some problems connected with the description of coexisting phases at low temperatures in Ising models. In: Lenard, A. (ed.) Mathematical Methods in Statistical Mechanics, pp. 162–202. Springer, Berlin (1973) CrossRefGoogle Scholar
  13. 13.
    Kotecký, R., Preiss, D.: Cluster expansion for abstract polymer systems. Commun. Math. Phys. 103, 491–498 (1986) zbMATHCrossRefADSGoogle Scholar
  14. 14.
    Lebowitz, J.L., Mazel, A.E.: A remark on the low temperature behavior of an SOS interface in half space. J. Stat. Phys. 84, 379–397 (1996) zbMATHCrossRefMathSciNetADSGoogle Scholar
  15. 15.
    Miracle-Sole, S.: On the convergence of cluster expansions. Physica A 279, 244–249 (2000) CrossRefMathSciNetADSGoogle Scholar
  16. 16.
    Sinai, Ya.G.: Theory of Phase Transitions: Rigorous Results. Pergamon Press, Oxford (1982) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Kenneth S. Alexander
    • 1
  • François Dunlop
    • 2
    Email author
  • Salvador Miracle-Solé
    • 3
  1. 1.Department of Mathematics KAP 108University of Southern CaliforniaLos AngelesUSA
  2. 2.Laboratoire de Physique Théorique et Modelisation (CNRS, UMR 8089)Université de Cergy-PontoiseCergy-PontoiseFrance
  3. 3.Centre de Physique ThéoriqueCNRSMarseille cedex 9France

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